# notation

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## 1—10 of 256 matching pages

##### 1: 32.1 Special Notation
###### §32.1 Special Notation
(For other notation see Notation for the Special Functions.) …
##### 2: 6.1 Special Notation
###### §6.1 Special Notation
(For other notation see Notation for the Special Functions.) … Unless otherwise noted, primes indicate derivatives with respect to the argument. …
##### 3: 1.1 Special Notation
###### §1.1 Special Notation
(For other notation see Notation for the Special Functions.) …
##### 4: 24.1 Special Notation
###### §24.1 Special Notation
(For other notation see Notation for the Special Functions.) …
###### Bernoulli Numbers and Polynomials
Among various older notations, the most common one is …
##### 5: 4.1 Special Notation
###### §4.1 Special Notation
(For other notation see Notation for the Special Functions.) … The main purpose of the present chapter is to extend these definitions and properties to complex arguments $z$. …
##### 6: 5.1 Special Notation
###### §5.1 Special Notation
(For other notation see Notation for the Special Functions.) … The notation $\Gamma\left(z\right)$ is due to Legendre. Alternative notations for this function are: $\Pi(z-1)$ (Gauss) and $(z-1)!$. Alternative notations for the psi function are: $\Psi(z-1)$ (Gauss) Jahnke and Emde (1945); $\Psi(z)$ Davis (1933); $\mathsf{F}(z-1)$ Pairman (1919). …
##### 7: 12.1 Special Notation
###### §12.1 Special Notation
(For other notation see Notation for the Special Functions.) … These notations are due to Miller (1952, 1955). …The notations are related by $U\left(a,z\right)=D_{-a-\frac{1}{2}}\left(z\right)$. Whittaker’s notation $D_{\nu}\left(z\right)$ is useful when $\nu$ is a nonnegative integer (Hermite polynomial case).
##### 8: 9.1 Special Notation
###### §9.1 Special Notation
(For other notation see Notation for the Special Functions.)
 $k$ nonnegative integer, except in §9.9(iii). …
Other notations that have been used are as follows: $\operatorname{Ai}\left(-x\right)$ and $\operatorname{Bi}\left(-x\right)$ for $\operatorname{Ai}\left(x\right)$ and $\operatorname{Bi}\left(x\right)$ (Jeffreys (1928), later changed to $\operatorname{Ai}\left(x\right)$ and $\operatorname{Bi}\left(x\right)$); $U(x)=\sqrt{\pi}\operatorname{Bi}\left(x\right)$, $V(x)=\sqrt{\pi}\operatorname{Ai}\left(x\right)$ (Fock (1945)); $A(x)=3^{-\ifrac{1}{3}}\pi\operatorname{Ai}\left(-3^{-\ifrac{1}{3}}x\right)$ (Szegő (1967, §1.81)); $e_{0}(x)=\pi\operatorname{Hi}(-x)$, $\widetilde{e}_{0}(x)=-\pi\operatorname{Gi}(-x)$ (Tumarkin (1959)).
##### 9: 8.1 Special Notation
###### §8.1 Special Notation
(For other notation see Notation for the Special Functions.) … Unless otherwise indicated, primes denote derivatives with respect to the argument. … Alternative notations include: Prym’s functions $P_{z}(a)=\gamma\left(a,z\right)$, $Q_{z}(a)=\Gamma\left(a,z\right)$, Nielsen (1906a, pp. 25–26), Batchelder (1967, p. 63); $(a,z)!=\gamma\left(a+1,z\right)$, $[a,z]!=\Gamma\left(a+1,z\right)$, Dingle (1973); $B(a,b,x)=\mathrm{B}_{x}\left(a,b\right)$, $I(a,b,x)=I_{x}\left(a,b\right)$, Magnus et al. (1966); $\operatorname{Si}\left(a,x\right)\to\operatorname{Si}\left(1-a,x\right)$, $\operatorname{Ci}\left(a,x\right)\to\operatorname{Ci}\left(1-a,x\right)$, Luke (1975).
##### 10: 7.1 Special Notation
###### §7.1 Special Notation
(For other notation see Notation for the Special Functions.) … Unless otherwise noted, primes indicate derivatives with respect to the argument. … Alternative notations are $Q(z)=\tfrac{1}{2}\operatorname{erfc}\left(z/\sqrt{2}\right)$, $P(z)=\Phi(z)=\tfrac{1}{2}\operatorname{erfc}\left(-z/\sqrt{2}\right)$, $\operatorname{Erf}z=\tfrac{1}{2}\sqrt{\pi}\operatorname{erf}z$, $\operatorname{Erfi}z=e^{z^{2}}F\left(z\right)$, $C_{1}(z)=C\left(\sqrt{2/\pi}z\right)$, $S_{1}(z)=S\left(\sqrt{2/\pi}z\right)$, $C_{2}(z)=C\left(\sqrt{2z/\pi}\right)$, $S_{2}(z)=S\left(\sqrt{2z/\pi}\right)$. The notations $P(z)$, $Q(z)$, and $\Phi(z)$ are used in mathematical statistics, where these functions are called the normal or Gaussian probability functions. …